Is there an equivalent "redshift" for cosmic rays due to expansion?

[Suekdccia]

TL;DR Summary

Is there an equivalent "redshift" for cosmic rays due to cosmological expansion?

I've found this discussion (https://astronomy.stackexchange.com...alent-of-the-red-shift-effect-for-cosmic-rays) where it is said that there is an equivalent redshift of cosmic rays due to the cosmic expansion

However, how can this be? Cosmic rays are not EM particles, so their wavelength should not be affected by the expansion of spacetime... And if it is affected by it, how does the expansion of the universe "steal" energy from cosmic rays? Does this then happen for all massive particles?

 

[Orodruin]

However, how can this be?

In a FLRW universe, the quantity $a(t) p$ is conserved for a test particle. When the scale factor grows, the momentum $p$ decreases.

Cosmic rays are not EM particles, so their wavelength should not be affected by the expansion of spacetime...

Yes they should.

And if it is affected by it, how does the expansion of the universe "steal" energy from cosmic rays?

Energy simply is not conserved in an expanding universe.

Does this then happen for all massive particles?

Yes.

 

[PAllen]

I can give you a synopsis of the math. How you interpret it is up to you - "expansion of space" is an interpretation, not tied to any mathematical object of GR.

Consider the generation of the cosmic ray far away, in the past light cone of 'us'. It is generated by some unknown "local" process, which as described in a local comoving inertial frame, gives energy E to the cosmic ray. Now parallel transport a tetrad representing that local frame along the cosmic ray path to us. This is local frame near us where the cosmic ray has energy E. However, our local frame will have a large velocity relative to this transported frame, so that we will measure a much lower energy for the cosmic ray.

Note that cosmological redshift can be derived with an essentially identical procedure.

There is no stealing of energy or stretching of light in this derivation.

 

[Suekdccia]

In a FLRW universe, the quantity $a(t) p$ is conserved for a test particle. When the scale factor grows, the momentum $p$ decreases.


Yes they should.


Energy simply is not conserved in an expanding universe.


Yes.

So do all massive particles tend to rest in an expanding universe? And does this occur in a universe with Λ=0?

 

[Bandersnatch]

So do all massive particles tend to rest in an expanding universe? And does this occur in a universe with Λ=0?

Yes, to both. All such massive particles join the local Hubble flow. The Davis and Lineweaver paper on the tethered galaxy problem includes some analysis of this.
It's important to stress that this is not due to some force acting to brake the mass, but as a result of arriving in a region where its erstwhile local velocity begins to match the recession velocity.

 

[Suekdccia]

It's important to stress that this is not due to some force acting to brake the mass, but as a result of arriving in a region where its erstwhile local velocity begins to match the recession velocity

But the particles lose energy arriving at that state. Can they recover it? Or as photons it is lost forever? Is there any form of energy that is not "redshifted" as spacetime expands?

 

[Orodruin]

But the particles lose energy arriving at that state.

The energy of a particle is a local frame dependent concept, not a global one. Saying that the particles lose energy is not really physically meaningful.

Can they recover it?

See above.

Or as photons it is lost forever? Is there any form of energy that is not "redshifted" as spacetime expands?

See above.

 

[Suekdccia]

In a FLRW universe, the quantity a(t)p is conserved for a test particle. When the scale factor grows, the momentum p decreases.

Does angular momentum also decrease?

 

[PAllen]

Does angular momentum also decrease?

The magnitude of angular momentum is invariant like mass of a particle. Neither gets red shifted.

 

[Suekdccia]

The magnitude of angular momentum is invariant like mass of a particle. Neither gets red shifted.

Do cosmic rays have angular momentum? Are there processes with a very high/energetic angular momentum in the universe?

Also, when matter is accreted by a black hole, it loses angular momentum to fall from the orbit closer to the black hole, but the orbiting speed of the particles would be higher. Would these velocities also be redshifted by expansion? Or being a local and bound system, expansion does not have any effects?

 

[Ibix]

Do cosmic rays have angular momentum?

Anything that isn't moving directly towards or away from you has angular momentum around your location.

 

[PAllen]

Anything that isn't moving directly towards or away from you has angular momentum around your location.

Yes, but I was thinking of spin angular momentum rather than orbital. The latter is frame dependent, the former is not ( in magnitude - it is in direction, obviously). Cosmic rays being primarily fermions would have intrinsic angular momentum. A spinning pulsar with huge peculiar velocity would also have a spin angular momentum that does not redshift.

 

[PAllen]

Also, when matter is accreted by a black hole, it loses angular momentum to fall from the orbit closer to the black hole, but the orbiting speed of the particles would be higher. Would these velocities also be redshifted by expansion? Or being a local and bound system, expansion does not have any effects?

This would be a highly bound system, so expansion would be irrelevant.

 

[Suekdccia]

A spinning pulsar with huge peculiar velocity would also have a spin angular momentum that does not redshift.

And the peculiar velocity would be the one redshifted correct?

 

[PAllen]

And the peculiar velocity would be the one redshifted correct?

Yes, when it reached us it would have much lower peculiar velocity than it had when it was ejected somehow from a galaxy (for example).

Note, this is exactly what @Bandersnatch explained in post: post #5